## Bernoulli

• Bernoulli
• Volume 25, Number 2 (2019), 1045-1075.

### Properties of switching jump diffusions: Maximum principles and Harnack inequalities

#### Abstract

This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated operators for switching jump diffusions are non-local, resulting in more difficulty in treating such systems. Our study is carried out by taking into consideration of the interplay of stochastic processes and the associated systems of integro-differential equations.

#### Article information

Source
Bernoulli, Volume 25, Number 2 (2019), 1045-1075.

Dates
Revised: July 2017
First available in Project Euclid: 6 March 2019

https://projecteuclid.org/euclid.bj/1551862843

Digital Object Identifier
doi:10.3150/17-BEJ1012

Mathematical Reviews number (MathSciNet)
MR3920365

Zentralblatt MATH identifier
07049399

#### Citation

Chen, Xiaoshan; Chen, Zhen-Qing; Tran, Ky; Yin, George. Properties of switching jump diffusions: Maximum principles and Harnack inequalities. Bernoulli 25 (2019), no. 2, 1045--1075. doi:10.3150/17-BEJ1012. https://projecteuclid.org/euclid.bj/1551862843

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